Batman definitely did not "get down on catwoman." There have been writers (for the TV show for example) who basically didn't get Batman and there's an element of sexual tension on the old Adam West serial. But unlike Superman and his female counterparts (LL, LL, WW etc) where the attraction is reciprocal and consistent, with canonical Batman there's a traditional understanding that while Batman is an object of lust for Catwoman, it's not strongly reciprocated.
The 14 year olds in you will post that it's because Catwoman is "evil" therefore Batman cant get with her but that's not the motivation. First of all, there's no prohibition in comics of a hero hooking up with an antihero... among superhero couplings, it's almost as common for a hero to get with an anithero as with a hero... Spidey/Black Cat etc. If you understand anything about Batman, it has to do with his emotional detachment and the transference of his PRIVATE feelings and emotional connections only being able to be expressed in a GENERAL love/emotional attachment to Gotham City as a surrogate... ergo his obsession with saving Gotham.
This is not only with Catwoman. Even with Dick Grayson there's a strong undercurrent/conflict of Batman not being "checked in" in his emotional dealings. Or even his dealings with his most trusted partner Superman... whose relationship is portrayed as conflict almost as often as it is partnership. the man simply cannot form normal emotional attachments nor express it in day to day life. he's certainly not going to express it sexually
and to Capt Picard above me... you make not like it but clearly Batman's tradition of pedastry in the comics leaves open the analogy to Sparta. it doesn't mean he is definitely gay but logically it leaves the door open. keep in mind that before the 20th century the idea of being "gay" as we know it didn't exist. Spartan dudes had wives and heirs and regular lives and packing fudge was just something they did sometimes it didn't "define" them. IMHO Batman is not actually gay... he's ascetic and it's possible that his development ******ed and his sexuality never concretely developed (the only thing he can "love" is Gothan). But be mature. It's not like Capt Picards has to beam in whenever someone raises that legitimate point
as for sex it's obvious. for all the reasons above Batman isn't going to have sex as a means to express emotional connections. The only other reason is for pleasure. And if any of you noobs can actually post that Batman... a man who dedicates his life to discipline and the NEGATION of PLEASURE in pursuit of his ideals is going to engage in the most hedonistic activities for no reason other than pleasure... well you're smart keep posting
the riddler and joker and all those cats however... have "gotten down" on catwoman as has a cast of thousands... if that makes you feel any better